It seems like a pretty common thing. Phone Support has already hung up me and I don't have time to hang out and wait again so I'm going to post for the time being.
Bought the CC today. I previous had an old copy of CS6 on here running as a trial. I got a new computer, migrated, and the Adobe Suite didn't get registered. After 3 weeks, today, I decided to go ahead and upgrade to the Creative Cloud.
After purchasing, download the App, signed in, and all the apps listed as "Download Trial". Thought that was weird and installed, sure enough, they all opened as trials. When I clicked to sign in it just asks for a serial number.
I hit the forums and found a suggestion and link for "AdobeCreativeCloudCleanerTool.dmg" which cleans out current and past Adobe Apps and license info. Ran that, uninstalled everything, started over.
This time when I install the Creative Suite App all the apps said "Download" instead of "Download Trial". Glimmer of Hope.
NOPE! They installed as trials again.
As a suggestion from another help post, I logged out, quite, restarted. It asked me to sign in and eventuall enter a serial number again.